Let's break down and simplify the expression:

The given expression is:

\[
55xy^2 + 110x^2y - 220x^2y^2m
\]

### Step 1: Identify Common Factors
We notice that the greatest common factor (GCF) for all three terms is **55**.

We can factor out **55** from the expression:

\[
55(xy^2 + 2x^2y - 4x^2y^2m)
\]

### Step 2: Simplification
Now, the factored expression is:

\[
55(xy^2 + 2x^2y - 4x^2y^2m)
\]

This is the simplified form of the given expression.

Would you like to explore further or ask for a specific part in more detail?

Here are 5 related questions:
1. How can we factor quadratic terms more generally?
2. What methods are there for finding the greatest common factor?
3. How would we factor if there were no common factors between terms?
4. Can we solve for specific values of \(x\), \(y\), and \(m\) in this expression?
5. How do we handle expressions involving multiple variables when simplifying?

**Tip:** Always check for the greatest common factor (GCF) first when simplifying algebraic expressions—it helps simplify the process.

Learn how to factor and simplify the algebraic expression 55xy^2 + 110x^2y - 220x^2y^2m by identifying the greatest common factor (GCF) and reducing the terms. This problem is ideal for students in Grades 9-10 and explores key algebraic concepts like factoring and simplification.

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